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Welcome to the first lesson in your CEM 11+ Non-Verbal Reasoning course! Shape sequences are one of the most important NVR question types. In a sequence question you are shown a series of shapes that follow a pattern, and you must work out what comes next (or which shape fills a gap in the sequence).
In the CEM exam, NVR questions are interleaved with maths questions, so you may encounter a sequence question between two number problems. The shapes can be unfamiliar and the patterns may change from year to year, so learning a reliable strategy is essential.
A shape sequence is a row of shapes (usually 4 or 5) arranged in order. Each shape changes from the one before it according to one or more rules. Your task is to identify those rules and predict the next shape.
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 |
|---|---|---|---|---|
| Small white circle | Medium white circle | Large white circle | ? |
Here the rule is simple: the circle gets bigger at each step. The answer for position 4 would be an even larger white circle.
When you look at a sequence, shapes can change in many different ways. Here are the main properties to watch:
| Property | What to look for |
|---|---|
| Shape type | Does the shape change from a circle to a triangle to a square? |
| Size | Does the shape get bigger, smaller, or alternate? |
| Shading | Does the fill change (black, white, grey, striped, dotted)? |
| Rotation | Does the shape turn by a fixed amount (e.g. 45 or 90 degrees)? |
| Number of sides | Do the sides increase (triangle, square, pentagon, hexagon)? |
| Position | Does a dot, line, or small shape move around inside the main shape? |
| Number of elements | Does an extra line, dot, or shape get added each step? |
The simplest sequences change only one property at a time.
| Step 1 | Step 2 | Step 3 | Step 4 | Step 5 |
|---|---|---|---|---|
| Arrow pointing up | Arrow pointing right | Arrow pointing down | Arrow pointing left | ? |
Rule: The arrow rotates 90 degrees clockwise each step.
Answer: The arrow returns to pointing up (the pattern cycles every 4 steps).
| Step 1 | Step 2 | Step 3 | Step 4 | Step 5 |
|---|---|---|---|---|
| Black square | Grey square | White square | Black square | ? |
Rule: The shading follows a three-step cycle: black, grey, white, then back to black.
Answer: Grey square.
In harder CEM questions, two or more properties change at the same time. You need to track each property separately.
| Step 1 | Step 2 | Step 3 | Step 4 |
|---|---|---|---|
| Small black triangle | Large white triangle | Small black triangle | ? |
Rule 1 (size): Alternates between small and large.
Rule 2 (shading): Alternates between black and white.
Answer: Large white triangle (large because the previous was small; white because the previous was black).
| Step 1 | Step 2 | Step 3 | Step 4 |
|---|---|---|---|
| Triangle with a dot at the top | Square with a dot on the right | Pentagon with a dot at the bottom | ? |
Rule 1 (shape): The number of sides increases by 1 each step.
Rule 2 (dot position): The dot moves clockwise around the shape: top, right, bottom, left.
Answer: Hexagon (6 sides) with a dot on the left.
It is important to understand the difference between these two types of pattern:
| Pattern type | How it works | Example |
|---|---|---|
| Progressive | A property keeps changing in one direction | Circle gets bigger and bigger at each step |
| Cyclic | A property repeats after a fixed number of steps | Shading goes black, grey, white, black, grey, white... |
Many CEM sequences combine both. For instance, the number of sides might increase progressively (3, 4, 5, 6...) while the shading cycles (black, white, black, white...).
Follow these steps every time you see a sequence question:
| Term | Meaning |
|---|---|
| Sequence | A set of shapes arranged in order following a rule |
| Rule | The pattern or change that happens from one step to the next |
| Cycle | A pattern that repeats after a fixed number of steps |
| Progressive | A pattern that keeps changing in one direction (e.g. getting bigger) |
| Rotation | Turning a shape around a point |
| Shading | The fill of a shape (black, white, grey, striped, etc.) |
Shape sequences ask you to find the pattern and predict what comes next. Check every property — shape, size, shading, rotation, position, and count. Track each property separately, especially when two or more rules are in play. Practise looking at unfamiliar shapes with confidence, and remember that the CEM exam can present sequences in unexpected ways. The more you practise, the faster you will spot the rules!